Okay, Aida is one of my favourite shows and Amneris is one of my (many) dream roles
You need to show a really strong high belt in an uptempo piece, more important than the lower range with Amneris, but it'd still be worth having a section of two in the song that is fairly low.
Look into roles that Amneris' of the past have played - Cathy L5Y, Catherine (???) Dirty Rotten Scoundrels etc and pick some of their big songs to investigate.
"here i am" from DRS is very much Amneris in terms of her personality and materialistic way of being
it also shows off a huge range, which is important
HOwever, it's probably gonna be very overdone, so i'd personally try to find something in that style... i'd suggest "Sumemr in ohio" from the L5Y but it'd have the same problem...
That reminds me, you should look into "the drowsy chaperone" and other shows that Sutton Foster has been leading lady material in. She's got that high belt, and you can exaggerate the "fashionista" side of the characters
any song to do with showing off or appearance to outsiders would work for Amneris, as her part is very comic in contrast to Aida. She also has to be quite unlikeable without being obviously "nasty"... she's a real person, and i'd play her as someone completely oblivious to the outside world... if that makes sense. She's just ignorant
If you have an acting audition, to show you can do the more bitter and serious side of the character, choose a more bitchy and dramatic monologue rather than comic